How would I calculate this problem. plz help I don't know how to...
An online store that has been successfully growing on its initial angel investment and revenues wants to invest $5 million to expand the business. The bank is willing to lend the business this money at a 10 percent interest rate over an eight-year term. Calculate the monthly payment, and explain what the business must be able to do with this money in order for this to be a smart business decision.
The above formula gives the amount of compounded (monthly) interest earned over an 8-year period, but does not provide the payment needed to amortize the loan.
That formula for monthly payment m is
m = Pr/(1 - (1+r)^-n)
In this case, we have
m = 5000000(.10/12)/(1 - (1+.10/12)^(-12*8))
= 75,870.82
P(1+ r/n)^nt
t = 8
Monthly n = 12
rate = 10%
thank you so much!
thank you! ,Steve
To calculate the monthly payment for the loan, you can use the formula for calculating loan payments:
M = P[r(1+r)^n]/[(1+r)^n-1]
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of months (loan term in years multiplied by 12)
In this case, the principal amount (P) is $5 million, the annual interest rate (r) is 10%, and the loan term (n) is 8 years.
First, let's calculate the monthly interest rate (r) by dividing the annual interest rate by 12:
r = 10% / 12 = 0.1/12 = 0.0083 (rounded to four decimal places)
Next, let's calculate the total number of months (n):
n = 8 years * 12 = 96 months
Now, we have all the values needed to calculate the monthly payment (M):
M = $5,000,000 * [0.0083(1+0.0083)^96] / [(1+0.0083)^96-1]
M = $5,000,000 * 0.84191 / 0.33648
M ≈ $12,468.19
Therefore, the monthly payment for the loan would be approximately $12,468.19.
To determine whether this is a smart business decision, the company needs to evaluate how it plans to use the $5 million to generate revenue and cover the loan payments. They should consider factors such as:
1. Return on investment (ROI): Will the investment generate sufficient returns to cover the loan payments and provide additional profit?
2. Growth potential: Will the expansion boost sales and profitability enough to justify the loan?
3. Market analysis: Are there favorable market conditions for the business to expand successfully?
4. Risk assessment: How risky is the investment? Are there mitigating factors or alternative strategies that can address potential risks?
By analyzing these considerations and conducting a thorough cost-benefit analysis, the business can determine whether taking the loan and making the investment is a wise decision.